\newproblem{lay:5_1_2}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 5.1.2}
	\end{large}
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Yolanda Manrique Marcos, Dec. 17th, 2013} \\}{}

  % Problem statement

    Is $\lambda=-3$ an eigenvalue of $\left|\begin{array}{cc}-1 & 4 \\ 6 & 9\end{array}\right|$? Why or why not?
}
   % Solution
	{
	To check whether $\lambda=-3$ is an eigenvalue or not, we test whether it is a solution of the equation
	\begin{center}
	$\left|\left(\begin{array}{cc}-1 & 4 \\ 6 & 9\end{array}\right)-\lambda I\right|=0 \Leftrightarrow$ \\
		$\left|\left(\begin{array}{cc}-1 & 4 \\ 6 & 9\end{array}\right)-(-3) \left(\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right)\right|=0\Leftrightarrow$ \\
		$\left|\begin{array}{cc}2 & 4 \\ 6 & 12\end{array}\right|=0 \Leftrightarrow$\\
		$0=0$\\
	\end{center}
	Since we have got an identity ($0=0$), $\lambda=-3$ is a solution of the eigenvalue problem and it is an eigenvalue of the proposed matrix.
}
\useproblem{lay:5_1_2}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}

